Question

1. if $\overrightarrow{uw}$ bisects $\angle tuv$, $m\angle tuw = (13x - 5)\degree$ and $m\angle wuv = (7x + 31)\degree$, find the value of $x$.

Explanation:

Step1: Recall Angle Bisector Definition

Since \(\overrightarrow{UW}\) bisects \(\angle TUV\), \(\angle TUW=\angle WUV\). So we set the two angle expressions equal: \(13x - 5=7x + 31\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides: \(13x-7x - 5=7x-7x + 31\), which simplifies to \(6x - 5 = 31\).
Add 5 to both sides: \(6x - 5+5 = 31+5\), so \(6x=36\).
Divide both sides by 6: \(\frac{6x}{6}=\frac{36}{6}\), giving \(x = 6\).

Answer:

\(x = 6\)